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GRED 505 (Topics in Mathematics for Elementary Teachers)
Assignment 7: Discovering numbers and concepts of special
importance in mathematics
Exploration 1. A (just born) pair of rabbits is placed in a walled enclosure. During the
first month of their life the rabbits produce no offspring. They reproduce one new pair of
rabbits at the age of 1 month and another new pair of rabbits at the age of 2 months. If
each new pair of rabbits reproduces in the same manner, how many pairs of rabbits will
be produced by the end of one year? (The production of offspring is pictured in Figure 1:
N – new pair, O – old pair)
Figure 1. Production of offspring over the five-month span
Exploration 2. How many different combinations of two-sided (red and yellow) counters
in which no two red counters appear in a row can be constructed with one, two, three,
four, five, etc. counters? Draw a diagram (picture) to support your exploration.
Exploration 3. Buildings of different number of stories are given and one has to color
them with a fixed color in such a way that no two consecutive stories are colored with it.
How many ways of such coloring of one, two, three, four, etc.–storied buildings are
possible? Note: non-coloring stories at all is considered as a special case of coloring (see
Figure 2).
Figure 2. All ways of coloring one-and two-storied buildings
Instructor Sergei Abramovich
